55:
251:
1470:
184:
His Caught A Herring" (tangent, sine, cosine) or "The Old Army
Colonel And His Son Often Hiccup" (tangent, cosine, sine) or "Come And Have Some Oranges Help To Overcome Amnesia" (cosine, sine, tangent). Communities in Chinese circles may choose to remember it as TOA-CAH-SOH, which also means 'big-footed woman' (
183:
Another method is to expand the letters into a sentence, such as "Some Old Horses Chew Apples
Happily Throughout Old Age", "Some Old Hippy Caught Another Hippy Tripping On Acid", or "Studying Our Homework Can Always Help To Obtain Achievement". The order may be switched, as in "Tommy On A Ship Of
952:
1077:
1026:
851:
1243:
1303:
1134:
1660:
1414:
686:
1370:
730:
1193:
887:
637:
777:
1798:
1456:
1574:
3175:
3128:
2971:
2924:
2767:
2720:
2563:
2516:
2359:
2312:
2155:
2108:
1922:
1860:
1712:
495:
3081:
2877:
2673:
2469:
2265:
2061:
3217:
3013:
2809:
2605:
2401:
2197:
582:
555:
528:
3042:
2838:
2634:
2430:
2226:
2022:
893:
1032:
981:
3555:
806:
1199:
1249:
446:
laws. These have the disadvantages of not going sequentially from quadrants 1 to 4 and not reinforcing the numbering convention of the quadrants.
3470:
1083:
3586:
1581:
3442:
3381:
3324:
1376:
648:
281:
of the plane. The letters ASTC signify which of the trigonometric functions are positive, starting in the top right 1st quadrant and moving
1477:
Another mnemonic permits all of the basic identities to be read off quickly. The hexagonal chart can be constructed with a little thought:
1332:
692:
3516:
3402:
3371:
1163:
857:
1578:
Going either clockwise or counter-clockwise, the starting vertex equals the next vertex divided by the vertex after that. For example,
1717:
3261:
159:
588:
3230:
3548:
242:) for O/H, A/H, O/A. Longer mnemonics for these letters include "Oscar Has A Hold On Angie" and "Oscar Had A Heap of Apples."
74:
ratios in a right triangle can be remembered by representing them as strings of letters, for instance SOH-CAH-TOA in
English:
3432:
1716:
The sum of the squares of the two items at the top of a triangle equals the square of the item at the bottom. These are the
3711:
3649:
736:
278:
1729:
3737:
3541:
3573:
1420:
1532:
209:
An alternate way to remember the letters for Sin, Cos, and Tan is to memorize the syllables Oh, Ah, Oh-Ah (i.e.
3134:
3087:
2930:
2883:
2726:
2679:
2522:
2475:
2318:
2271:
2114:
2067:
1866:
1804:
1667:
54:
39:
471:
274:
43:
3048:
2844:
2640:
2436:
2232:
2028:
250:
3181:
2977:
2773:
2569:
2365:
2161:
3732:
3613:
3462:
3675:
3639:
1469:
561:
534:
193:
3603:
1929:
Aside from the last bullet, the specific values for each identity are summarized in this table:
1433:
1267:
1101:
912:
749:
615:
3644:
3492:
3438:
3377:
3341:
3320:
3289:
3267:
3257:
3508:
3410:
513:
453:
still goes counterclockwise but starts in quadrant 4 going through quadrants 4, 1, 2, then 3.
3685:
3021:
2817:
2613:
2409:
2205:
2001:
282:
212:
185:
124:
3591:
1482:
947:{\displaystyle \;\,{\frac {1}{2}}\;{\Big /}{\frac {\sqrt {3}}{2}}={\frac {1}{\sqrt {3}}}}
1072:{\displaystyle {\frac {\sqrt {\mathbf {\color {green}{2}} }}{2}}={\frac {1}{\sqrt {2}}}}
1021:{\displaystyle {\frac {\sqrt {\mathbf {\color {green}{2}} }}{2}}={\frac {1}{\sqrt {2}}}}
1494:
Write the functions without "co" on the three left outer vertices (from top to bottom:
3314:
459:
still starts in quadrant 1 but goes clockwise going through quadrants 1, 4, 3, then 2.
17:
3726:
3581:
3376:. Spectrum series. Washington, DC: Mathematical Association of America. p. 119.
846:{\displaystyle {\frac {\sqrt {\mathbf {\color {teal}{1}} }}{2}}=\;\,{\frac {1}{2}}}
31:
3373:
Twenty years before the blackboard: the lessons and humor of a mathematics teacher
3344:
1664:
The starting corner equals the product of its two nearest neighbors. For example,
3448:
1481:
Draw three triangles pointing down, touching at a single point. This resembles a
1238:{\displaystyle {\frac {\sqrt {\mathbf {\color {teal}{1}} }}{2}}=\;{\frac {1}{2}}}
3680:
3665:
468:
Sines and cosines of common angles 0°, 30°, 45°, 60° and 90° follow the pattern
3292:
1298:{\displaystyle {\frac {\sqrt {3}}{2}}{\Big /}\;{\frac {1}{2}}\;\,={\sqrt {3}}}
3349:
3297:
3271:
1129:{\displaystyle {\frac {1}{\sqrt {2}}}{\Big /}{\frac {1}{\sqrt {2}}}=\;\;1}
3565:
3251:
270:
172:
35:
1655:{\displaystyle \sin A={\frac {\cos A}{\cot A}}={\frac {\tan A}{\sec A}}}
1509:
Write the co-functions on the corresponding three right outer vertices (
121:
One way to remember the letters is to sound them out phonetically (i.e.
3706:
3634:
3598:
1485:
203:
58:
Image mnemonic to help remember the ratios of sides of a right triangle
1529:
The starting vertex equals one over the opposite vertex. For example,
1409:{\displaystyle {\frac {\sqrt {\mathbf {\color {blue}{0}} }}{2}}=\;\,0}
681:{\displaystyle {\frac {\sqrt {\mathbf {\color {blue}{0}} }}{2}}=\;\;0}
3701:
3629:
1365:{\displaystyle {\frac {\sqrt {\mathbf {\color {red}{4}} }}{2}}=\;\,1}
725:{\displaystyle {\frac {\sqrt {\mathbf {\color {red}{4}} }}{2}}=\;\;1}
3533:
3256:. Fiona McGill. Cheltenham: Stanley Thornes Publishers. p. 51.
310:
Quadrant 4 (angles from 270 to 360 degrees, or 3π/2 to 2π radians):
303:
Quadrant 3 (angles from 180 to 270 degrees, or π to 3π/2 radians):
3608:
1468:
1188:{\displaystyle {\frac {\sqrt {\mathbf {\color {orange}{3}} }}{2}}}
882:{\displaystyle {\frac {\sqrt {\mathbf {\color {orange}{3}} }}{2}}}
249:
53:
296:
Quadrant 2 (angles from 90 to 180 degrees, or π/2 to π radians):
3537:
289:
Quadrant 1 (angles from 0 to 90 degrees, or 0 to π/2 radians):
632:{\displaystyle \tan \theta =\sin \theta {\Big /}\cos \theta }
307:
angent and cotangent functions are positive in this quadrant.
3494:
Precalculus with Limits: A Graphing
Approach, Texas Edition
234:
228:
220:
215:
151:
148:
139:
133:
314:
osine and secant functions are positive in this quadrant.
300:
ine and cosecant functions are positive in this quadrant.
1491:
Write a 1 in the middle where the three triangles touch
293:
trigonometric functions are positive in this quadrant.
3184:
3137:
3090:
3051:
3024:
2980:
2933:
2886:
2847:
2820:
2776:
2729:
2682:
2643:
2616:
2572:
2525:
2478:
2439:
2412:
2368:
2321:
2274:
2235:
2208:
2164:
2117:
2070:
2031:
2004:
1869:
1807:
1732:
1670:
1584:
1535:
1423:
1379:
1335:
1252:
1202:
1166:
1086:
1035:
984:
896:
860:
809:
739:
695:
651:
591:
564:
537:
516:
474:
160:
136:
130:
127:
145:
3694:
3658:
3622:
3572:
225:
142:
3211:
3169:
3122:
3075:
3036:
3007:
2965:
2918:
2871:
2832:
2803:
2761:
2714:
2667:
2628:
2599:
2557:
2510:
2463:
2424:
2395:
2353:
2306:
2259:
2220:
2191:
2149:
2102:
2055:
2016:
1916:
1854:
1792:
1706:
1654:
1568:
1450:
1408:
1364:
1297:
1237:
1187:
1128:
1071:
1020:
946:
881:
845:
771:
724:
680:
631:
576:
549:
522:
489:
254:Signs of trigonometric functions in each quadrant.
3431:Heng, H. H.; Cheng, Khoo; Talbert, J. F. (2005).
1525:Starting at any vertex of the resulting hexagon:
1994:... equals the product of two nearest neighbors
772:{\displaystyle \;\;0\;\;{\Big /}\;\;1\;\;=\;\;0}
1793:{\displaystyle \sin ^{2}A+\cos ^{2}A=1^{2}=1\ }
3549:
3437:. Pearson Education South Asia. p. 228.
8:
3403:"Sine, Cosine and Tangent in Four Quadrants"
3463:"Math Mnemonics and Songs for Trigonometry"
3283:
3281:
1451:{\displaystyle \;\;1\;\;{\Big /}\;\;0\;\;=}
231:
3556:
3542:
3534:
3370:Stueben, Michael; Sandford, Diane (1998).
1569:{\displaystyle \sin A={\frac {1}{\csc A}}}
1444:
1443:
1439:
1438:
1430:
1429:
1425:
1424:
1401:
1357:
1283:
1272:
1224:
1122:
1121:
909:
897:
831:
765:
764:
760:
759:
755:
754:
746:
745:
741:
740:
718:
717:
674:
673:
42:and the relationships between the various
3397:
3395:
3393:
3365:
3363:
3361:
3183:
3170:{\displaystyle ={\frac {\csc A}{\cot A}}}
3141:
3136:
3123:{\displaystyle ={\frac {\tan A}{\sin A}}}
3094:
3089:
3055:
3050:
3023:
2979:
2966:{\displaystyle ={\frac {\cot A}{\cos A}}}
2937:
2932:
2919:{\displaystyle ={\frac {\sec A}{\tan A}}}
2890:
2885:
2851:
2846:
2819:
2775:
2762:{\displaystyle ={\frac {\cos A}{\sin A}}}
2733:
2728:
2715:{\displaystyle ={\frac {\csc A}{\sec A}}}
2686:
2681:
2647:
2642:
2615:
2571:
2558:{\displaystyle ={\frac {\sin A}{\tan A}}}
2529:
2524:
2511:{\displaystyle ={\frac {\cot A}{\csc A}}}
2482:
2477:
2443:
2438:
2411:
2367:
2354:{\displaystyle ={\frac {\tan A}{\sec A}}}
2325:
2320:
2307:{\displaystyle ={\frac {\cos A}{\cot A}}}
2278:
2273:
2239:
2234:
2207:
2163:
2150:{\displaystyle ={\frac {\sec A}{\csc A}}}
2121:
2116:
2103:{\displaystyle ={\frac {\sin A}{\cos A}}}
2074:
2069:
2035:
2030:
2003:
1917:{\displaystyle \tan ^{2}A+1=\sec ^{2}A\ }
1899:
1874:
1868:
1855:{\displaystyle 1+\cot ^{2}A=\csc ^{2}A\ }
1837:
1818:
1806:
1775:
1756:
1737:
1731:
1707:{\displaystyle \sin A=\cos A\cdot \tan A}
1669:
1626:
1597:
1583:
1548:
1534:
1432:
1431:
1422:
1402:
1385:
1383:
1380:
1378:
1358:
1341:
1339:
1336:
1334:
1288:
1284:
1273:
1266:
1265:
1253:
1251:
1225:
1208:
1206:
1203:
1201:
1172:
1170:
1167:
1165:
1106:
1100:
1099:
1087:
1085:
1057:
1041:
1039:
1036:
1034:
1006:
990:
988:
985:
983:
932:
917:
911:
910:
899:
898:
895:
866:
864:
861:
859:
833:
832:
815:
813:
810:
808:
748:
747:
738:
701:
699:
696:
694:
657:
655:
652:
650:
614:
613:
590:
563:
536:
515:
475:
473:
438:Other easy-to-remember mnemonics are the
1931:
507:
3242:
490:{\displaystyle {\frac {\sqrt {n}}{2}}}
1040:
989:
656:
7:
3076:{\displaystyle ={\frac {1}{\cos A}}}
2872:{\displaystyle ={\frac {1}{\sin A}}}
2668:{\displaystyle ={\frac {1}{\tan A}}}
2464:{\displaystyle ={\frac {1}{\sec A}}}
2260:{\displaystyle ={\frac {1}{\csc A}}}
2056:{\displaystyle ={\frac {1}{\cot A}}}
1718:trigonometric Pythagorean identities
1171:
865:
3509:"Magic Hexagon for Trig Identities"
3212:{\displaystyle =\csc A\cdot \tan A}
3008:{\displaystyle =\cot A\cdot \sec A}
2804:{\displaystyle =\cos A\cdot \csc A}
2600:{\displaystyle =\sin A\cdot \cot A}
2396:{\displaystyle =\cos A\cdot \tan A}
2192:{\displaystyle =\sin A\cdot \sec A}
464:Sines and cosines of special angles
1384:
1207:
814:
25:
3316:Memory: A Very Short Introduction
1473:Trigonometric identities mnemonic
1340:
700:
3231:List of trigonometric identities
1386:
1342:
1209:
1173:
1042:
991:
867:
816:
702:
658:
211:
123:
3519:from the original on 2018-02-05
3497:(6 ed.). Cengage Learning.
3473:from the original on 2019-10-17
1991:counter-clockwise/anticlockwise
198:
3650:List of biochemistry mnemonics
1:
3253:Key Maths : GCSE, Higher
3313:Foster, Jonathan K. (2008).
577:{\displaystyle \cos \theta }
550:{\displaystyle \sin \theta }
3712:List of chemistry mnemonics
3754:
505:for cosine, respectively:
285:through quadrants 2 to 4.
246:All Students Take Calculus
3671:Mnemonics in trigonometry
318:Other mnemonics include:
189:
40:trigonometric identities
27:Mathematical memory aids
3319:. Oxford. p. 128.
523:{\displaystyle \theta }
275:trigonometric functions
44:trigonometric functions
3434:Additional Mathematics
3250:Humble, Chris (2001).
3213:
3171:
3124:
3077:
3038:
3037:{\displaystyle \sec A}
3009:
2967:
2920:
2873:
2834:
2833:{\displaystyle \csc A}
2805:
2763:
2716:
2669:
2630:
2629:{\displaystyle \cot A}
2601:
2559:
2512:
2465:
2426:
2425:{\displaystyle \cos A}
2397:
2355:
2308:
2261:
2222:
2221:{\displaystyle \sin A}
2193:
2151:
2104:
2057:
2018:
2017:{\displaystyle \tan A}
1918:
1856:
1794:
1708:
1656:
1570:
1474:
1452:
1410:
1366:
1299:
1239:
1189:
1130:
1073:
1022:
948:
883:
847:
773:
726:
682:
633:
578:
551:
524:
491:
255:
59:
34:, it is common to use
18:Trigonometry mnemonics
3214:
3172:
3125:
3078:
3039:
3010:
2968:
2921:
2874:
2835:
2806:
2764:
2717:
2670:
2631:
2602:
2560:
2513:
2466:
2427:
2398:
2356:
2309:
2262:
2223:
2194:
2152:
2105:
2058:
2019:
1919:
1857:
1795:
1709:
1657:
1571:
1472:
1453:
1411:
1367:
1300:
1240:
1190:
1131:
1074:
1023:
949:
884:
848:
774:
727:
683:
634:
579:
552:
525:
492:
273:for the sign of each
253:
57:
3614:Thermodynamic square
3491:Larson, Ron (2014).
3467:Online Math Learning
3182:
3135:
3088:
3049:
3022:
2978:
2931:
2884:
2845:
2818:
2774:
2727:
2680:
2641:
2614:
2570:
2523:
2476:
2437:
2410:
2366:
2319:
2272:
2233:
2206:
2162:
2115:
2068:
2029:
2002:
1867:
1805:
1730:
1668:
1582:
1533:
1421:
1377:
1333:
1250:
1200:
1164:
1084:
1033:
982:
894:
858:
807:
737:
693:
649:
589:
562:
535:
514:
472:
3604:Planetary mnemonic
3342:Weisstein, Eric W.
3290:Weisstein, Eric W.
3209:
3167:
3120:
3073:
3034:
3005:
2963:
2916:
2869:
2830:
2801:
2759:
2712:
2665:
2626:
2597:
2555:
2508:
2461:
2422:
2393:
2351:
2304:
2257:
2218:
2189:
2147:
2100:
2053:
2014:
1914:
1852:
1790:
1704:
1652:
1566:
1475:
1448:
1406:
1390:
1362:
1346:
1295:
1235:
1213:
1185:
1177:
1126:
1069:
1046:
1018:
995:
944:
879:
871:
843:
820:
769:
722:
706:
678:
662:
629:
574:
547:
520:
487:
256:
60:
3738:Science mnemonics
3720:
3719:
3645:Taxonomy mnemonic
3444:978-981-235-211-8
3383:978-0-88385-525-6
3326:978-0-19-280675-8
3222:
3221:
3165:
3118:
3071:
2961:
2914:
2867:
2757:
2710:
2663:
2553:
2506:
2459:
2349:
2302:
2255:
2145:
2098:
2051:
1935:Starting function
1913:
1851:
1789:
1650:
1621:
1564:
1462:
1461:
1396:
1392:
1352:
1348:
1293:
1281:
1263:
1259:
1233:
1219:
1215:
1183:
1179:
1116:
1115:
1097:
1096:
1067:
1066:
1052:
1048:
1016:
1015:
1001:
997:
942:
941:
927:
923:
907:
877:
873:
841:
826:
822:
712:
708:
668:
664:
485:
481:
38:to help remember
16:(Redirected from
3745:
3558:
3551:
3544:
3535:
3528:
3527:
3525:
3524:
3505:
3499:
3498:
3488:
3482:
3481:
3479:
3478:
3459:
3453:
3452:
3447:. Archived from
3428:
3422:
3421:
3419:
3418:
3409:. Archived from
3399:
3388:
3387:
3367:
3356:
3355:
3354:
3337:
3331:
3330:
3310:
3304:
3303:
3302:
3285:
3276:
3275:
3247:
3218:
3216:
3215:
3210:
3176:
3174:
3173:
3168:
3166:
3164:
3153:
3142:
3129:
3127:
3126:
3121:
3119:
3117:
3106:
3095:
3082:
3080:
3079:
3074:
3072:
3070:
3056:
3043:
3041:
3040:
3035:
3014:
3012:
3011:
3006:
2972:
2970:
2969:
2964:
2962:
2960:
2949:
2938:
2925:
2923:
2922:
2917:
2915:
2913:
2902:
2891:
2878:
2876:
2875:
2870:
2868:
2866:
2852:
2839:
2837:
2836:
2831:
2810:
2808:
2807:
2802:
2768:
2766:
2765:
2760:
2758:
2756:
2745:
2734:
2721:
2719:
2718:
2713:
2711:
2709:
2698:
2687:
2674:
2672:
2671:
2666:
2664:
2662:
2648:
2635:
2633:
2632:
2627:
2606:
2604:
2603:
2598:
2564:
2562:
2561:
2556:
2554:
2552:
2541:
2530:
2517:
2515:
2514:
2509:
2507:
2505:
2494:
2483:
2470:
2468:
2467:
2462:
2460:
2458:
2444:
2431:
2429:
2428:
2423:
2402:
2400:
2399:
2394:
2360:
2358:
2357:
2352:
2350:
2348:
2337:
2326:
2313:
2311:
2310:
2305:
2303:
2301:
2290:
2279:
2266:
2264:
2263:
2258:
2256:
2254:
2240:
2227:
2225:
2224:
2219:
2198:
2196:
2195:
2190:
2156:
2154:
2153:
2148:
2146:
2144:
2133:
2122:
2109:
2107:
2106:
2101:
2099:
2097:
2086:
2075:
2062:
2060:
2059:
2054:
2052:
2050:
2036:
2023:
2021:
2020:
2015:
1990:
1988:
1987:
1984:
1981:
1971:
1969:
1968:
1965:
1962:
1953:
1951:
1950:
1947:
1944:
1932:
1923:
1921:
1920:
1915:
1911:
1904:
1903:
1879:
1878:
1861:
1859:
1858:
1853:
1849:
1842:
1841:
1823:
1822:
1799:
1797:
1796:
1791:
1787:
1780:
1779:
1761:
1760:
1742:
1741:
1713:
1711:
1710:
1705:
1661:
1659:
1658:
1653:
1651:
1649:
1638:
1627:
1622:
1620:
1609:
1598:
1575:
1573:
1572:
1567:
1565:
1563:
1549:
1457:
1455:
1454:
1449:
1437:
1436:
1415:
1413:
1412:
1407:
1397:
1391:
1389:
1382:
1381:
1371:
1369:
1368:
1363:
1353:
1347:
1345:
1338:
1337:
1326:
1324:
1323:
1320:
1317:
1316:
1304:
1302:
1301:
1296:
1294:
1289:
1282:
1274:
1271:
1270:
1264:
1255:
1254:
1244:
1242:
1241:
1236:
1234:
1226:
1220:
1214:
1212:
1205:
1204:
1194:
1192:
1191:
1186:
1184:
1178:
1176:
1169:
1168:
1157:
1155:
1154:
1151:
1148:
1147:
1135:
1133:
1132:
1127:
1117:
1111:
1107:
1105:
1104:
1098:
1092:
1088:
1078:
1076:
1075:
1070:
1068:
1062:
1058:
1053:
1047:
1045:
1038:
1037:
1027:
1025:
1024:
1019:
1017:
1011:
1007:
1002:
996:
994:
987:
986:
975:
973:
972:
969:
966:
965:
953:
951:
950:
945:
943:
937:
933:
928:
919:
918:
916:
915:
908:
900:
888:
886:
885:
880:
878:
872:
870:
863:
862:
852:
850:
849:
844:
842:
834:
827:
821:
819:
812:
811:
800:
798:
797:
794:
791:
790:
778:
776:
775:
770:
753:
752:
731:
729:
728:
723:
713:
707:
705:
698:
697:
687:
685:
684:
679:
669:
663:
661:
654:
653:
638:
636:
635:
630:
619:
618:
583:
581:
580:
575:
556:
554:
553:
548:
529:
527:
526:
521:
508:
504:
503:n = 4, 3, ..., 0
500:
499:n = 0, 1, ..., 4
496:
494:
493:
488:
486:
477:
476:
283:counterclockwise
241:
240:
237:
236:
233:
230:
227:
223:
222:
218:
217:
200:
191:
167:
163:
158:
157:
154:
153:
150:
147:
144:
141:
138:
135:
132:
129:
21:
3753:
3752:
3748:
3747:
3746:
3744:
3743:
3742:
3723:
3722:
3721:
3716:
3690:
3654:
3618:
3592:Right-hand rule
3568:
3562:
3532:
3531:
3522:
3520:
3507:
3506:
3502:
3490:
3489:
3485:
3476:
3474:
3461:
3460:
3456:
3445:
3430:
3429:
3425:
3416:
3414:
3401:
3400:
3391:
3384:
3369:
3368:
3359:
3340:
3339:
3338:
3334:
3327:
3312:
3311:
3307:
3288:
3287:
3286:
3279:
3264:
3249:
3248:
3244:
3239:
3227:
3180:
3179:
3154:
3143:
3133:
3132:
3107:
3096:
3086:
3085:
3060:
3047:
3046:
3020:
3019:
2976:
2975:
2950:
2939:
2929:
2928:
2903:
2892:
2882:
2881:
2856:
2843:
2842:
2816:
2815:
2772:
2771:
2746:
2735:
2725:
2724:
2699:
2688:
2678:
2677:
2652:
2639:
2638:
2612:
2611:
2568:
2567:
2542:
2531:
2521:
2520:
2495:
2484:
2474:
2473:
2448:
2435:
2434:
2408:
2407:
2364:
2363:
2338:
2327:
2317:
2316:
2291:
2280:
2270:
2269:
2244:
2231:
2230:
2204:
2203:
2160:
2159:
2134:
2123:
2113:
2112:
2087:
2076:
2066:
2065:
2040:
2027:
2026:
2000:
1999:
1985:
1982:
1979:
1978:
1976:
1966:
1963:
1960:
1959:
1957:
1948:
1945:
1942:
1941:
1939:
1895:
1870:
1865:
1864:
1833:
1814:
1803:
1802:
1771:
1752:
1733:
1728:
1727:
1666:
1665:
1639:
1628:
1610:
1599:
1580:
1579:
1553:
1531:
1530:
1483:fallout shelter
1467:
1419:
1418:
1375:
1374:
1331:
1330:
1321:
1318:
1314:
1313:
1312:
1310:
1248:
1247:
1198:
1197:
1162:
1161:
1152:
1149:
1145:
1144:
1143:
1141:
1082:
1081:
1031:
1030:
980:
979:
970:
967:
963:
962:
961:
959:
892:
891:
856:
855:
805:
804:
795:
792:
788:
787:
786:
784:
735:
734:
691:
690:
647:
646:
643:0° = 0 radians
587:
586:
560:
559:
533:
532:
512:
511:
502:
498:
470:
469:
466:
248:
224:
219:
214:
210:
181:
165:
161:
126:
122:
52:
28:
23:
22:
15:
12:
11:
5:
3751:
3749:
3741:
3740:
3735:
3725:
3724:
3718:
3717:
3715:
3714:
3709:
3704:
3698:
3696:
3692:
3691:
3689:
3688:
3683:
3678:
3673:
3668:
3662:
3660:
3656:
3655:
3653:
3652:
3647:
3642:
3637:
3632:
3626:
3624:
3620:
3619:
3617:
3616:
3611:
3606:
3601:
3596:
3595:
3594:
3589:
3587:Left-hand rule
3578:
3576:
3570:
3569:
3563:
3561:
3560:
3553:
3546:
3538:
3530:
3529:
3500:
3483:
3454:
3451:on 2023-06-10.
3443:
3423:
3389:
3382:
3357:
3345:"Trigonometry"
3332:
3325:
3305:
3277:
3262:
3241:
3240:
3238:
3235:
3234:
3233:
3226:
3223:
3220:
3219:
3208:
3205:
3202:
3199:
3196:
3193:
3190:
3187:
3177:
3163:
3160:
3157:
3152:
3149:
3146:
3140:
3130:
3116:
3113:
3110:
3105:
3102:
3099:
3093:
3083:
3069:
3066:
3063:
3059:
3054:
3044:
3033:
3030:
3027:
3016:
3015:
3004:
3001:
2998:
2995:
2992:
2989:
2986:
2983:
2973:
2959:
2956:
2953:
2948:
2945:
2942:
2936:
2926:
2912:
2909:
2906:
2901:
2898:
2895:
2889:
2879:
2865:
2862:
2859:
2855:
2850:
2840:
2829:
2826:
2823:
2812:
2811:
2800:
2797:
2794:
2791:
2788:
2785:
2782:
2779:
2769:
2755:
2752:
2749:
2744:
2741:
2738:
2732:
2722:
2708:
2705:
2702:
2697:
2694:
2691:
2685:
2675:
2661:
2658:
2655:
2651:
2646:
2636:
2625:
2622:
2619:
2608:
2607:
2596:
2593:
2590:
2587:
2584:
2581:
2578:
2575:
2565:
2551:
2548:
2545:
2540:
2537:
2534:
2528:
2518:
2504:
2501:
2498:
2493:
2490:
2487:
2481:
2471:
2457:
2454:
2451:
2447:
2442:
2432:
2421:
2418:
2415:
2404:
2403:
2392:
2389:
2386:
2383:
2380:
2377:
2374:
2371:
2361:
2347:
2344:
2341:
2336:
2333:
2330:
2324:
2314:
2300:
2297:
2294:
2289:
2286:
2283:
2277:
2267:
2253:
2250:
2247:
2243:
2238:
2228:
2217:
2214:
2211:
2200:
2199:
2188:
2185:
2182:
2179:
2176:
2173:
2170:
2167:
2157:
2143:
2140:
2137:
2132:
2129:
2126:
2120:
2110:
2096:
2093:
2090:
2085:
2082:
2079:
2073:
2063:
2049:
2046:
2043:
2039:
2034:
2024:
2013:
2010:
2007:
1996:
1995:
1992:
1973:
1954:
1936:
1927:
1926:
1925:
1924:
1910:
1907:
1902:
1898:
1894:
1891:
1888:
1885:
1882:
1877:
1873:
1862:
1848:
1845:
1840:
1836:
1832:
1829:
1826:
1821:
1817:
1813:
1810:
1800:
1786:
1783:
1778:
1774:
1770:
1767:
1764:
1759:
1755:
1751:
1748:
1745:
1740:
1736:
1722:
1721:
1714:
1703:
1700:
1697:
1694:
1691:
1688:
1685:
1682:
1679:
1676:
1673:
1662:
1648:
1645:
1642:
1637:
1634:
1631:
1625:
1619:
1616:
1613:
1608:
1605:
1602:
1596:
1593:
1590:
1587:
1576:
1562:
1559:
1556:
1552:
1547:
1544:
1541:
1538:
1523:
1522:
1507:
1492:
1489:
1466:
1463:
1460:
1459:
1447:
1442:
1435:
1428:
1416:
1405:
1400:
1395:
1388:
1372:
1361:
1356:
1351:
1344:
1328:
1306:
1305:
1292:
1287:
1280:
1277:
1269:
1262:
1258:
1245:
1232:
1229:
1223:
1218:
1211:
1195:
1182:
1175:
1159:
1137:
1136:
1125:
1120:
1114:
1110:
1103:
1095:
1091:
1079:
1065:
1061:
1056:
1051:
1044:
1028:
1014:
1010:
1005:
1000:
993:
977:
955:
954:
940:
936:
931:
926:
922:
914:
906:
903:
889:
876:
869:
853:
840:
837:
830:
825:
818:
802:
780:
779:
768:
763:
758:
751:
744:
732:
721:
716:
711:
704:
688:
677:
672:
667:
660:
644:
640:
639:
628:
625:
622:
617:
612:
609:
606:
603:
600:
597:
594:
584:
573:
570:
567:
557:
546:
543:
540:
530:
519:
484:
480:
465:
462:
461:
460:
454:
436:
435:
417:
400:
383:
378:eachers (are)
366:
348:
334:
316:
315:
308:
301:
294:
247:
244:
180:
177:
119:
118:
104:
90:
51:
48:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3750:
3739:
3736:
3734:
3731:
3730:
3728:
3713:
3710:
3708:
3705:
3703:
3700:
3699:
3697:
3693:
3687:
3684:
3682:
3679:
3677:
3674:
3672:
3669:
3667:
3664:
3663:
3661:
3657:
3651:
3648:
3646:
3643:
3641:
3638:
3636:
3633:
3631:
3628:
3627:
3625:
3621:
3615:
3612:
3610:
3607:
3605:
3602:
3600:
3597:
3593:
3590:
3588:
3585:
3584:
3583:
3580:
3579:
3577:
3575:
3571:
3567:
3559:
3554:
3552:
3547:
3545:
3540:
3539:
3536:
3518:
3514:
3510:
3504:
3501:
3496:
3495:
3487:
3484:
3472:
3468:
3464:
3458:
3455:
3450:
3446:
3440:
3436:
3435:
3427:
3424:
3413:on 2015-01-18
3412:
3408:
3404:
3398:
3396:
3394:
3390:
3385:
3379:
3375:
3374:
3366:
3364:
3362:
3358:
3352:
3351:
3346:
3343:
3336:
3333:
3328:
3322:
3318:
3317:
3309:
3306:
3300:
3299:
3294:
3291:
3284:
3282:
3278:
3273:
3269:
3265:
3263:0-7487-3396-5
3259:
3255:
3254:
3246:
3243:
3236:
3232:
3229:
3228:
3224:
3206:
3203:
3200:
3197:
3194:
3191:
3188:
3185:
3178:
3161:
3158:
3155:
3150:
3147:
3144:
3138:
3131:
3114:
3111:
3108:
3103:
3100:
3097:
3091:
3084:
3067:
3064:
3061:
3057:
3052:
3045:
3031:
3028:
3025:
3018:
3017:
3002:
2999:
2996:
2993:
2990:
2987:
2984:
2981:
2974:
2957:
2954:
2951:
2946:
2943:
2940:
2934:
2927:
2910:
2907:
2904:
2899:
2896:
2893:
2887:
2880:
2863:
2860:
2857:
2853:
2848:
2841:
2827:
2824:
2821:
2814:
2813:
2798:
2795:
2792:
2789:
2786:
2783:
2780:
2777:
2770:
2753:
2750:
2747:
2742:
2739:
2736:
2730:
2723:
2706:
2703:
2700:
2695:
2692:
2689:
2683:
2676:
2659:
2656:
2653:
2649:
2644:
2637:
2623:
2620:
2617:
2610:
2609:
2594:
2591:
2588:
2585:
2582:
2579:
2576:
2573:
2566:
2549:
2546:
2543:
2538:
2535:
2532:
2526:
2519:
2502:
2499:
2496:
2491:
2488:
2485:
2479:
2472:
2455:
2452:
2449:
2445:
2440:
2433:
2419:
2416:
2413:
2406:
2405:
2390:
2387:
2384:
2381:
2378:
2375:
2372:
2369:
2362:
2345:
2342:
2339:
2334:
2331:
2328:
2322:
2315:
2298:
2295:
2292:
2287:
2284:
2281:
2275:
2268:
2251:
2248:
2245:
2241:
2236:
2229:
2215:
2212:
2209:
2202:
2201:
2186:
2183:
2180:
2177:
2174:
2171:
2168:
2165:
2158:
2141:
2138:
2135:
2130:
2127:
2124:
2118:
2111:
2094:
2091:
2088:
2083:
2080:
2077:
2071:
2064:
2047:
2044:
2041:
2037:
2032:
2025:
2011:
2008:
2005:
1998:
1997:
1993:
1974:
1955:
1937:
1934:
1933:
1930:
1908:
1905:
1900:
1896:
1892:
1889:
1886:
1883:
1880:
1875:
1871:
1863:
1846:
1843:
1838:
1834:
1830:
1827:
1824:
1819:
1815:
1811:
1808:
1801:
1784:
1781:
1776:
1772:
1768:
1765:
1762:
1757:
1753:
1749:
1746:
1743:
1738:
1734:
1726:
1725:
1724:
1723:
1719:
1715:
1701:
1698:
1695:
1692:
1689:
1686:
1683:
1680:
1677:
1674:
1671:
1663:
1646:
1643:
1640:
1635:
1632:
1629:
1623:
1617:
1614:
1611:
1606:
1603:
1600:
1594:
1591:
1588:
1585:
1577:
1560:
1557:
1554:
1550:
1545:
1542:
1539:
1536:
1528:
1527:
1526:
1520:
1516:
1512:
1508:
1505:
1501:
1497:
1493:
1490:
1487:
1484:
1480:
1479:
1478:
1471:
1465:Hexagon chart
1464:
1445:
1440:
1426:
1417:
1403:
1398:
1393:
1373:
1359:
1354:
1349:
1329:
1308:
1307:
1290:
1285:
1278:
1275:
1260:
1256:
1246:
1230:
1227:
1221:
1216:
1196:
1180:
1160:
1139:
1138:
1123:
1118:
1112:
1108:
1093:
1089:
1080:
1063:
1059:
1054:
1049:
1029:
1012:
1008:
1003:
998:
978:
957:
956:
938:
934:
929:
924:
920:
904:
901:
890:
874:
854:
838:
835:
828:
823:
803:
782:
781:
766:
761:
756:
742:
733:
719:
714:
709:
689:
675:
670:
665:
645:
642:
641:
626:
623:
620:
610:
607:
604:
601:
598:
595:
592:
585:
571:
568:
565:
558:
544:
541:
538:
531:
517:
510:
509:
506:
501:for sine and
482:
478:
463:
458:
455:
452:
449:
448:
447:
445:
441:
433:
429:
425:
421:
418:
415:
411:
407:
404:
401:
398:
394:
390:
387:
384:
381:
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3681:Piphilology
3659:Mathematics
3630:CHON/CHNOPS
3513:Math is Fun
3407:Math Is Fun
3293:"SOHCAHTOA"
1975:... equals
1956:... equals
1938:... equals
50:SOH-CAH-TOA
3727:Categories
3523:2018-02-04
3477:2019-10-17
3417:2015-01-18
3237:References
1458:undefined
199:tōa-kha-só
194:Pe̍h-ōe-jī
113:pposite ÷
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3564:Science
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3471:Archived
3272:47985033
3225:See also
1949:opposite
1327:radians
1158:radians
976:radians
801:radians
325:tations
279:quadrant
277:in each
271:mnemonic
261:tudents
173:Krakatoa
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3635:ESCAPPM
3623:Biology
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3378:ISBN
3321:ISBN
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399:lass
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